RTTI in Delphi has always been important since version 1.0. Classic RTTI features include the "published" properties section of Classes, which allowed the Object Inspector and the component designtime features to work. For my purposes, I would often use Published class properties to allow for enumeration of those properties at runtime. To store things from my objects to disk, for persistence.
The Delphi 2010 RTTI extends this classic RTTI massively, so much so that you could be forgiven for thinking Delphi did not even have RTTI until delphi 2010.
I would say the #1 most useful applications of "The New RTTI" are (as several other answers already state) going to be in Frameworks written by the gurus, that:
Handle persistence to files or databases. Database and configuration or document saving/loading frameworks and components would use this under the hood.
Handle pickling/marshalling/encoding/decoding to and from various
over-the-wire formats, like JSON, XML, EDI, and other things.
Unit testing was mentioned by someone else (JUnit), but I think perhaps the same frameworks could be really handy for debug and error reporting tools. Given an object passed as a parameter, on the stack, why not have bug reports that can dump all the data that was passed along to a function that failed, and not just a list of functions?